The course introduces the basic concepts and methods of probability. Topics include: probability spaces, random variables, distributions, law of large numbers, central limit theorem, random walk, Markov chains and martingales in discrete time, and if time allows diffusion processes including Brownian motion.

The course will build on infinite series, multivariable calculus, basics about linear algebra, and along the way we will introduce the required notions about set theory and elementary measure theory.

Problem sets:

Will be available on this page,
usually to be submitted for grading every week. Must be submitted before
the end of class. Counts for 40% of the course grade. Two lowest
homework scores will be dropped.